三维广义MHD方程和Boussinesq方程正则性准则的注记  

Remarks on Regularity Criteria for 3D Generalized MHD Equations and Boussinesq Equations

作　　者：邱华 谢常平 房少梅[1,2] Hua Qiu;Changping Xie;Shaomei Fang(College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642;School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100)

机构地区：[1]华南农业大学数学与信息学院,广州510642 [2]长江师范学院数学与统计学院,重庆408100

出　　处：《数学物理学报（A辑）》2019年第2期316-328,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11126266;11271141);广东省自然科学基金(2016A030313390);国家留学基金委员会~~

摘　　要：该文研究三维具有分数阶耗散项的广义MHD方程,得到了在负指标齐次Besov空间意义下速度场u与磁场b和的正则性准则,推广了已有结论.另外,该文还得到了三维分数阶耗散广义Boussinesq方程光滑解关于速度梯度的一个正则性准则.In this paper, we study the 3D generalized MHD system with dissipation and diffusion in terms of fractional Laplacian. We obtain a regularity criterion of solution for the generalized MHD equations in terms of the summation of velocity field u and magnetic field b under the framework of homogeneous Besov space with negative indices, which extends the previous results. We also present a regularity criterion of smooth solution to the 3D generalized Boussinesq equations with fractional dissipation in terms of the gradient of velocity only.

关 键 词：广义MHD方程 广义BOUSSINESQ方程 正则性准则 BESOV空间 

分 类 号：O175.2[理学—数学]